Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function φ(Z) = Q − ZPZ′ is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this ...

Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ which involve a large number of agents that weakly coupled via weighted undirected graph on each node represents an agent. The links the correspond couplings between agents' dynamics, as well individual cost functions, agent attempts minimize. We formulate limit LQ-GFG problems based assumption these graphs lie in sequence conv...

This study investigates the efficacy of optimal semi-active dampers for achieving the best results in seismic response mitigation of adjacent buildings connected to each other by magnetorheological (MR) dampers under earthquakes. One of the challenges in the application of this study is to develop an effective optimal control strategy that can fully utilize the capabilities of the MR dampers. H...

Leaching of a low-grade lead and zinc oxide ore was studied by an organic reagent, citric acid. The quadratic mathematical models were developed for the relationship among the influential parameters and lead and zinc recoveries. Leaching rate was strongly affected by the interactive effects of factors. It was also found that the quadratic effects of stirring speed and linear<e...